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જો $\,|\mathop A\limits^ \to \,\, \times \,\,\mathop B\limits^ \to |\,\, = \,\,\sqrt 3 \,\,\mathop A\limits^ \to .\mathop B\limits^ \to $ હોય તો $\,|\mathop A\limits^ \to \, + \,\mathop B\limits^ \to |$ નું મૂલ્ય શું થશે ?
${\left( {{A^2}\,\, + \;\,{B^2}\,\, + \,\,\frac{{AB}}{{\sqrt 3 }}} \right)^{1/2}}$
$A + B$
${\left( {{A^2}\,\, + \,\,{B^2}\,\, + \;\,\sqrt 3 \,\,AB} \right)^{1/2}}$
${\left( {{A^2}\,\, + \,\,{B^2}\,\, + \;\,AB} \right)^{1/2}}$
Solution
$|\mathop A\limits^ \to \,\, \times \,\,\mathop B\limits^ \to |\,\, = \,\,\sqrt 3 \,\,\mathop A\limits^ \to .\mathop B\limits^ \to $
$AB\sin \theta \,\, = \,\,\sqrt 3 \,AB\cos \,\,\theta \,\,\,$ અથવા $\tan \,\,\theta \,\, = \,\,\sqrt 3 \,\,\,\theta \,\, = \,\,60^\circ $
$|\mathop A\limits^ \to \, + \,\,\mathop B\limits^ \to |\,\, = \,\,{\left( {{A^2}\,\, + \;\,{B^2}\,\, + \;\,2AB\,\,\cos 60^\circ } \right)^{1/2}}\,\, = \,\,\,{\left( {{A^2}\,\, + \;\,{B^2}\,\, + \;\,AB} \right)^{1/2}}$
